Problem: $ D = \left[\begin{array}{rrr}1 & 2 & -1\end{array}\right]$ $ F = \left[\begin{array}{rr}1 & 2\end{array}\right]$ Is $ D- F$ defined?
Answer: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ D$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ D$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ D$ ) must equal $ q$ (number of columns in $ F$ Do $ D$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ D$ and $ F$ have the same number of columns? No Yes No No Since $ D$ has different dimensions $(1\times3)$ from $ F$ $(1\times2)$, $ D- F$ is not defined.